Inside the chamber at Thrihnukagigur in Iceland. Click on the magnifying glass icon for a photograph of an entry point. Photograph: K Maack

"Are you going into the volcano?" In any other country the question would be prefaced with "Good god, man!" and followed with a string of question and exclamation marks. But in Iceland it's a fairly normal question for anyone about to embark on the country's newest tour.

Launched last week, "Inside The Volcano" may sound like a ride at Alton Towers, but it is instead a very literal description of the dormant chamber of Thrihnukagigur, a volcanic peak just outside Reykjavik, which is now open to visitors. For the first time, intrepid travellers can climb over the rim and descend into the once-fiery abyss.

It has been 4,000 years since Thrihnukagigur last popped, and like all eruptions it was tremendously violent. Crucially, though, it wasn't so cataclysmic as to destroy the chamber and the entire mountain; instead the vast geological pressure was likely to have been vented through tunnels and arteries deeper in the earth, preserving a newly opened chamber and creating what cave explorer Arni Stefánsson describes as a "pristine collapse".

In 1974, Stefánsson was the first person to be lowered inside, and it was his idea to open up the mountain to tourists. Progress has been slow, but he says there is a tricky balance to be struck between opening the underworld and protecting the "single most important volcanic cave in the world". There are a few other accessible volcanoes – notably Furna do Enxofre in the Azores – but none so complete, nor so deep. This combination, along with the resolute focus on preservation, is what makes the mountain and the tour unique.

Located just 20km outside Reykjavik, Thrihnukagigur has huge potential as a day-trip destination from the capital, or even a side trip during a flight stopover – it is only about an hour from the main airport.

If the volcano tour proves popular, a tunnel may eventually – and carefully – be cut into it, and standing platforms installed inside. But for now, conquering the volcano requires a satisfying amount of effort. Just to reach it, we have to trek for 3km over uneven volcanic fields, past gas tunnels, fissures and small cones sculpted by volcanic forces just beneath the surface, with Thrihnukagigur, or Three Peaks, looming on the horizon.

When Eyjafjallajökull (which is 150km away) erupted in 2010, its ash clouds caused huge inconvenience to airline passengers around the world.

But that was insignificant compared with some volcanic incidents in Iceland's past. While in most of the world's volcanic regions the largest eruptions are the subject of ancient history, Iceland, a geological baby at 15m years old, has barely finished its tumultuous birth. Unfortunately, as in 2010, its most ferocious incidents are rarely contained within its borders.

Stefánsson describes the 1783 eruption of Laki, a mountain in the south of the island, as "immense", though apocalyptic would perhaps be more accurate.

The colossal gas emissions caused temperatures to soar in Europe, and led to thousands of deaths from sulphur dioxide inhalation, while North America subsequently suffered a long, cold winter because the sun's light was obscured. When the eruption finally ended, eight months later, Laki's fury had killed 25% of Iceland's population and half of its wildlife.

Stefánsson, my guide, is talking about these events as though something like Laki could happen again, at any time, especially as Iceland is due to enter one of its once-a-millennium periods of sustained volcanic activity. "But that's not inevitable, is it?" I ask, as we approach Thrihnukagigur. Stefánsson stops, looks as me as though I've insulted his mother, and says: "Absolutely. It will definitely happen."

This isn't what I want to hear just as I am about to enter Hades. Despite its relative calm, Stefánsson says that inside Thrihnukagigur there is also a real risk from earthquakes, which could easily dislodge rocks and crush visitors. "So it'll be the earthquakes that will get us, not another eruption," I say hopefully. "Oh no no," he replies. "It could definitely erupt, too."

This exchange takes place just before we climb on to a rickety platform ready to be lowered 120m into the throat of the volcano. I can't help wishing my host was a little less straight-talking.

Visitors are lowered 120m into the cave on a platform

When he did this as a 25-year-old, Stefánsson was alone, on a rope, spinning in the dark, and wearing a motorbike helmet for protection. Things have moved on a lot in 38 years, but even now it's not exactly a smooth process. The platform is fitted with tyres to help it pass a particularly narrow stretch 20m from the surface. As the natural light fades, the amount of water seeping through the porous rock increases. Down and down the platform goes, until it reaches the rocky floor.

"When I first got down here, I was so disappointed. It was nothing more than a quarry," says Stefánsson. "I came looking for beauty, but I found ugliness." He didn't come back for 17 years. When he finally returned – with better lighting and more time – he was overcome by a sense of wonderment. He now talks about the chamber with a kind of philosophical awe: "Coming here is a chance to feel your own smallness, to tackle your own fears. I want people to come here and feel humble."

For me, standing inside the volcano is a strangely emotional experience. First, there's the sheer unlikeliness of the situation – of standing in a site of unimaginable geological violence. Once that passes, there is an opportunity to enjoy the awesome subterranean arena. The rock dome has been scalded and charred, torn and ruptured; the gasses, pressures and extreme temperatures have stained it a mishmash of yellows, reds and blacks. It looks like a child's drawing of hell.

But inside there is not an increase of temperature as you might expect, nor any reek of sulphur. Instead, there is a stillness that creates a sense of tranquillity and, yes, smallness.

Stefánsson seems happy with my reaction. "Firstly this project is about preservation, then exploration, and finally education," he says over a bowl of hot soup back on the surface. "It's not about volcanology, really. It's about the aesthetic … It's about beauty."

• Tours are available until 31 July, but more dates may be added. The price is ISK 37,000pp (£188)including equipment and collection from Reykjavik. (+354 863 6640, insidethevolcano.com). Visitors must be over the age of 12, and have a reasonable level of fitness. The tour takes about five hours, including one hour inside the volcano. There are plans to make the visitor experience smoother, so go this year to feel more of a sense of exploration. Flights were provided by Iceland Express (0118-321 8384, icelandexpress.com), which flies to Reykjavik from Stansted, Gatwick and Edinburgh from £178 return. Accommodation was provided by Hotel Holt in central Reykjavik (+354 552 5700, holt.is, doubles from €143)